Here we go then...
Nobody really agrees on a definition of "language," so it's impossible to say whether something is or isn't, but this sort of thing is excluded by most defintions, and I can't see a defintion that includes it being a particularly useful one to have. One key thing that's missing here is communication - after all, these sounds clearly aren't being used to communicate with (untrained) mothers, and it seems very unlikely that there's any communication with peers going on. Which isn't to say that communication has to be part of the definition of language - it's perfectly possible to exclude these baby sounds using, for instance, a more structural defintion.
What do you mean by reflexive?
Exactly (although it's debateable how referential human language is). And it's even simpler than a myoclonic jerk - as you can tell from the "explanations" for the hunger and tiredness sounds, it's basically just the result of an instinctive reflex (e.g. yawning) combined with vocalising. You could presumably extend this to things like the discomfort sound, which might result from heavy breathing, and so on, all though all this is speculative and should really be scrutinised by phoneticists and others to confirm it.
I guess you're thinking of things like vervet monkeys, which have different calls to alert the group about different types of predators, which does seem more like human language, albeit still very far off. And there aren't very many examples like this.
Yeah, although it does misrepresent things a bit, which isn't a good way of doing science. The research has potential to be interesting/useful though.